I'm given that an ideal $I=\langle F_1, F_2, F_3, F_4, F_5, F_6, F_7\rangle$
$F_1=a+b+c-d-e-f$
$F_2=a+b+c-g-h-i$
$F_3=a+b+c-g-e-c$
$F_4=a+b+c-a-e-i$
$F_5=a+d+g-a-e-i$
$F_6=a+d+g-c-f-i$
$F_7=a+d+g-b-e-h$
I've computed the Groebner Basis as $\{3f-4g-h+2i, e-f+g-i, d-f+2g-2i, c+f-g-h, b+f-2g, a+f-2g-h+i\}$
How can I use this result to determine if a given polynomial $F$ is in $I$